P-, I-, g-, and D-Angles in Normed Spaces

Gunawan, Hendra; Lindiarni, Janny; Neswan, Oki

doi:10.5614/itbj.sci.2008.40.1.3

Cited by 11 publications

(15 citation statements)

References 4 publications

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“…Gunawan, Lindiarni and Neswan (cf. [44]) defined two angle functions preserving orthogonality types: the P-angle, which preserves Pythagorean orthogonality, and the I-angle, which preserves isosceles orthogonality. Thürey (cf.…”

Section: Angles Preserving Orthogonality Typesmentioning

confidence: 99%

Angles in normed spaces

et al. 2016

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The concept of angle, angle functions, and the question how to measure angles present old and well-established mathematical topics referring to Euclidean space, and there exist also various extensions to non-Euclidean spaces of different types. In particular, it is very interesting to investigate or to combine (geometric) properties of possible concepts of angle functions and angle measures in finite-dimensional real Banach spaces (= Minkowski spaces). However, going into this direction one will observe that there is no monograph or survey reflecting the complete picture of the existing literature on such concepts in a satisfying manner. We try to close this gap. In this expository paper (containing also new results, and new proofs of known results) the reader will get a comprehensive overview of this field, including also further related aspects. For example, angular bisectors, their applications, and angle types which preserve certain kinds of orthogonality are discussed. The latter aspect yields, of course, an interesting link to the large variety of orthogonality types in such spaces.

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Section: Angles Preserving Orthogonality Typesmentioning

confidence: 99%

Angles in normed spaces

et al. 2016

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“…′′ 031) was obtained from the optical observations with the Hubble Space Telescope (HST) (Niemela et al 1998). It is interetsing to note that Setia Gunawan et al (2000) reported 3.38-year periodic variations superimposed on the 1.4-GHz slow rise in the radio emission from WR 146. However, as the authors stated these variations are too short to be the WR+O binary period and might be caused by a third, low-mass, object in the system.…”

Section: The Wolf-rayet Star Wr 146mentioning

confidence: 97%

X-rays from the colliding wind binary WR 146

Zhekov

2017

Monthly Notices of the Royal Astronomical Society

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The X-ray emission from the massive binary WR 146 is analysed in the framework of the colliding stellar wind (CSW) picture. The theoretical CSW model spectra match well the shape of the observed X-ray spectrum of WR 146 but they overestimate considerably the observed X-ray flux (emission measure). This is valid both in the case of complete temperature equalization and in the case of partial electron heating at the shock fronts (different electron and ion temperatures), but, there are indications for a better correspondence between model predictions and observations for the latter. To reconcile the model predictions and observations, the mass-loss rate of WR 146 must be reduced by a factor of 8 -10 compared to the currently accepted value for this object (the latter already takes clumping into account). No excess X-ray absorption is derived from the CSW modelling.

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“…From the above observations, we define an angle between x, y ∈ V, denote by ∠ • (x, y) (see [3,4,8], for more informations about this notions, and their elementary properties), by…”

Section: Elementary Properties Of V •mentioning

confidence: 99%

“…Suppose V is a real linear space, and in arbitrary normed spaces V := (V, · ), following [8,3], we define (Wilson) non-linear functional ·, · • : V × V → R, by x, y • := x 2 + y 2 − x − y 2 2 ,…”

Section: Introductionmentioning

confidence: 99%